How to multiply vector by scalar in material nodes?
You should think more about the data types. If you want vector*scalar, use MixRGB set to Multiply (an RGB color has three components, like a vector), and not a simple scalar math node. See my answer to this question for an example of vector*scalar: Scale Texture with a Value-/Math-Node

Also your selector seems to be a Mix Shader (I didn't download your file, but it has shader inputs and outputs), and you should not put scalars into a node that expects shaders.

EDIT Just for completeness: There are also other ways of doing vector*scalar, like using a vector Mapping node and setting the same X, Y, Z Scale, or separating the vector components with a Separate XYZ and multiplying the three scalar coordinates individually, and merging them again with Combine XYZ.